The problem of image restoration from noisy measurements as encountered in nuclear medicine is considered. A model for the emission/detection process is introduced, which is based on the Poisson statistics of the emissions and a point-spread function for the imaging system. A new approach for treating the measurements is given, in which they are represented by a spatial noncausal interaction model before maximum entropy restoration, which describes the statistical dependence among the image values and their neighbourhood. The particular application of the algorithms presented relates to gamma-ray imaging systems, and is aimed at improving the resolution-noise-suppression product. Results for actual gamma camera data are presented and compared with more conventional techniques.<>